A Unital Banach Algebra That Is Not a Calkin Algebra
The realisation problem asks which unital Banach algebras arise as the Calkin algebra $\mathcal{B}(X)/\mathcal{K}(X)$ of some Banach space. Recorded in Tarbard's thesis and studied by Horváth and Kania. The paper exhibits a unital Banach algebra that cannot be one.